The 84 elements found on Earth occur as 339 isotopes.
Only 269 of these are stable, and the other 70 are radioactive. An additional
1650 radioactive isotopes have been created in nuclear reactors and in particle
accelerators.

The following is a table of all 29 known radioactive isotopes that have a
half-life of one million years or more, and that are not being
continually produced by natural nuclear reactions. It has been sorted in
order of half-life. For each isotope, the table shows whether it is one of the
ones found on Earth.

The thing to notice is that this list falls naturally into two halves.
Short-lived radioactives are suspiciously absent from the Earth. If we had
carried this list all the way down to 1,000 year half-lives, the block of
no's would be 37 long instead of 10 long.

Of course, nothing about this list really proves that the Earth is old. But
the list is exactly what we would expect if the Earth is old, and it is a very
puzzling list if the Earth is young.

Footnotes:

The list is of isotopes not being continually produced on Earth. I
left out four isotopes because of this rule.

Manganese 53 and Beryllium 10 are produced by cosmic-ray radiation
hitting dust in the upper atmosphere.

Uranium 236 is produced in uranium ores by neutrons from other
radioactives.

Iodine 129 is produced from Tellurium 130 by cosmic-ray muons.

Radioactives with half-lives shorter than one million years are also
produced: for example, Carbon
14 with a half life of 5730 years. (return)

The missing isotopes could have been present when the Earth was
formed. It is reasonable to ask if they are missing because they were
somehow never created in the first place. The answer is that they are not
particularly difficult to produce "artificially", and current scientific
theories about stars and supernovas say that these elements should have been
produced in fairly large quantities. For example, Technetium 97 is in the
no list above, but it has been detected in stars. One recent scientific theory
about stars proposes how they manufacture Technetium 97 and also how
Supernova 1987a manufactured Cobalt-56. (Supernova 1987a was special
because it was not very far away. Theory predicts that such a supernova would
create about 0.1 solar masses of nickel-56, which is radioactive. Nickel-56
decays with a half-life of 6.1 days into cobalt-56, which in turn decays
with a half-life of 77.1 days. Both kinds of decay give off very distinctive
gamma rays. Analysis of the gamma rays from SN1987a showed mostly cobalt-56,
exactly as predicted. And, the amount of those gamma rays died away with
exactly the half-life of cobalt-56.)
(return)

The list is essentially compatible with the age many scientists propose for the
earth. That age is 4.55 billion years. For most practical purposes, a
radioactive material is no longer present after 10 or 20 of its half-lives.
This is because 210 is about a thousand, and 220 is
about a million. So, after 20 half-lives, only one millionth of the original
amount remains.

Uranium 235's half life is 704 million years, so 4.55 billion years is just
a bit over six half-lives. It's reasonable for Uranium 235 to still be around
in small quantities after that amount of time. And, in fact, it makes up about
one percent of the Uranium now on Earth. The amounts of Uranium 235 and
Uranium 238 would have been about equal, 4.55 billion years ago. (return)

Finding Plutonium 244. Its half life is 82 million years, so 4.55
billion years is 55 half lives. You might reasonably ask how come Plutonium
244 isn't listed as no. The answer is that someone made a very serious
effort to find it: their article is referenced below. Eighty five kilograms of
molybdenum ore were chemically concentrated, and then the lot was tediously
run through a mass spectrometer. The amount of Plutonium 244 they found,
10-14 grams, was so small that it would have averaged one single
radioactive decay every six years. Clearly, they could not have detected this
Plutonium 244 with a geiger counter. However, 55 half lives ago, it would have
been about one kilogram of plutonium metal. That's believable in 85 kilograms
of metal ore.

Samarium 146's half life is 103 million years, so 4.55 billion years is 44
half lives. This means that Samarium 146 could be 200 billion times rarer than
Uranium 235, but could be a thousand times commoner than Plutonium 244. I
predict that if anyone tries very very hard to find Samarium 146, they will
succeed. Curium 247, at almost 300 half lives, is completely out of the
question." (return)

Conclusion: In short, the cutoff point in the list of isotopes is consistent with a old earth.